CASE V. When the given price is in one denomination.

RULE. Multiply the quantity by the price, and the product will be the answer in the same name as the price;-if pence or shillings, reduce to pounds.

Note. This rule is general, but the exercises in this Case are of ten more readily calculated by one or other of the former Rules.

EXAMPLES.

Find the value of 768 lbs. at 7d., at 43/, and at £7.

CASE VI. When the price is in several denominations.

RULE. Multiply the quantity by the number of the highest deno

mination, and take parts of the quantity for the lower ones; the sum will be the answer; which reduce, if necessary, to pounds.

Or, Divide the price into such parts, as that one of them may be an aliquot part of 20/, or of 1/, and the rest either aliquot parts of 20, or of 1/, or of a part already found; then calculate for these severally, and the sum of the results is the answer; which, if necessary, reduce to pounds.

Note 1. When the price contains a fraction, you may multiply the price by the under figure of the fraction, or by any number that will exterminate the fraction; then calculate for this new price, and divide the value so found, by the same number by which you multiplied the given price, for the answer.

2. When we have to multiply by a whole number with a fraction annexed to it, it is often easiest to multiply by the next greater whole number, and then deduct from the product a part of the multiplicand, for the excess of the assumed above the given multiplier. Thus, suppose the given multiplier to be 92, we may multiply by 10, and then deduct from the product part of the mul tiplicand.

Find the value of 33. 816 lbs. at 5/11. 34. 975 lbs. at 6/63. 35. 759 lbs. at 6/91. 36. 618 lbs. at 7/7. 37. 474 lbs. at 7/10. 38. 727 lbs. at 8/43. 39. 633 lbs. at 9/1. 40. 796 lbs. at 11/9. 41. 974 lbs. at 12/10.

42. 845 lbs. at 14/1.

46.

47.

Find the value of
43. 682 lbs. at 15/7
44. 756 lbs. at 16/5.
45. 583 lbs. at 17/10.
908 lbs. at 18/3.
764 cwt. at 27/6.
48. 856 cwt. at 35/9.
49. 429 cwt. at 47/8.
50. 638 cwt. at 68/6.
51. 991 cwt. at 73/9.
52. 750 cwt. at 108/4.

CASE VII. When there is a fraction in the given quantity.

RULE. Calculate as before for the integral part, and to the result, add a proportional part of the price for the fraction.

Or, Esteem the integral part of the quantity to be pounds, and substitute for the fraction such a part of £1 as the fraction is of a unit; then take parts for the price, as before.

Note. A fraction may be considered in two ways: thus yard may be considered either as the fourth part of 3 yards, or as 3 times the 4th part of 1 yard: 7 lb. may be considered either as the 16th part of 7 lbs., or as 7 times the 16th part of 1 lb.

mul

CASE VIII. When the price may be converted into an easy

tiplier.

RULE. Esteem the quantity the price, and the price the quantity,

and then find the value by Compound Multiplication...

EXAMPLES.

Find the value of 1271⁄2 lbs. at 31⁄2d., at 5/10, and at 9/3.

CASE IX. When the quantity consists of several denominations.

RULE. Multiply the price by the number of the highest denomination, and take parts of the price for the lower denominations; then will the sum be the answer.

Or, Consider the number of the highest denomination as pounds, and instead of the lower denominations, substitute their value at the rate of £1 for 1 of the highest denomination; then calculate for the price, as before.

Note. The value of the lower denominations, which most fre quently occur in practice at the rate of £1 for 1 of the highest denomination may be found as follows:

At £1 per cwt. the value of 1 qr. is 5/, of 7 lbs. is 1/3, and of 1 lb. is 24 pence: thus, the value of 21 cwt. 2 qrs. 21 ĺbs. at £1, is £21: 13:9.

At £1 per ton, the value of 1 cwt is 1/, of 1 qr. is 3d, and of 7 lbs. is ad.: thus, the value of 53 tons 15 cwt. 3 qrs. 21 lbs. at £1, is £53: 15:11.

At £1 per oz. troy, the value of 1 dwt. is 1/, and of 1 gr. is ¿d.: thus, the value of 10 oz. 15 dwt. 21 gr. at £1, is £10: 15: 101. At £1 per acre, the value of 1 rood is 5/, of 1 pole or fall is 14d, and of 6 ells is d.: thus, the value of 25 ac. 3 r. 174 falls at £1, is £25: 17:21.

F

EXAMPLES.

Find the value of 19 cwt. 2 qrs. 21 lbs. at 67/6.

At £1 per cwt. it is £19 13 9

2 qr.£3 7 6x7

1. Find the value of 13 cwt. 1 qr. 7 lbs. at 28/6.
2. Find the value of 23 cwt. 2 qrs. 14 lbs. at 34/4.
3. Find the value of 32 cwt. 3 qrs. 21 lbs. at 42/6.
4. Find the value of 42 cwt. 1 qr. 16 lbs. at 55/.
5. Find the value of 53 cwt. 3 qrs. 17 lbs. at 63/7.
6. Find the value of 65 cwt. 2 qrs. 24 lbs. at 70/.
7. Find the value of 73 cwt. 1 qr. 10 lbs. at 82/3.
8. Find the value of 81 cwt. 2 qrs. 8 lbs. at 96/8.

9. Find the value of 17 tons 11 cwt. 3 qrs. at £35 : 15: 6.

10. Find the value of 31 tons 8 cwt. 13 lbs. at £57: 17: 9.

11. Find the value of 81 tons 18 cwt. 3 qrs. 14 lbs. at £23:13: 4. 12. Find the value of 9 oz. 13 dwt. 17 gr. at 77/10:

13. Find the value of 12 oz. 10 dwt. 12 gr. at 77/6.

14. Find the value of 23 ac. 1 rd. 16 poles, at £42: 10: 6.

15. Find the value of 37 ac. 3 rds. 21 falls, 19 ells, at £5:15:6.

16. Find the value of 97 ac. 2 rds. 17 falls, 12 ells, at £23:12:6.

17. Find the value of 5 hhds. 36 gallons, at £39: 10: 6.
18. Find the value of 17 ankers 7 gallons, at £6 : 18 : 6.
19. Find the value of 36 quarters 3 bushels, at 49/3.
20. Find the value of 99 dozen 5 pairs, at 67/99.

21. Find the value of 38 dozen 8 pairs, at 53/8.

22. Find the value of 17 miles 2 fur. 55 yds. at £126: 13:4. 23. Find the value of 121 roods 21 yds. 8 feet, at £7: 15: 3. 24. Find the value of 79 roods 33 yds. 5 feet, at 63/6.

MENTAL CALCULATIONS.

I. To find the value of a dozen of articles, when the price of 1 is given, reckon 1/ for every penny in the price. Thus, 12 lbs. at 9d. is=9/.